amy is 5 feet tall shes standing 12 feet from a street light if amy's shawdow is 4 feet long which porportion could be used to find the height of the street light
the ratio vertical:horizontal remains constant, so
5/4 = x/(12+4)
15
To find the height of the streetlight, we can use a proportion based on the length of Amy's shadow and her actual height.
Let's define:
A = Amy's height (in feet)
S_Amy = Length of Amy's shadow (in feet)
S_Streetlight = Length of the streetlight's shadow (in feet)
H_Streetlight = Height of the streetlight (unknown)
We have the following values:
A = 5 feet
S_Amy = 4 feet
S_Streetlight = unknown
H_Streetlight = unknown
We can set up a proportion based on the similarity of the two triangles formed by the shadow and the height of Amy and the streetlight:
Amy's height / Length of Amy's shadow = Height of the streetlight / Length of the streetlight's shadow
A / S_Amy = H_Streetlight / S_Streetlight
Now, we can substitute the known values:
5 feet / 4 feet = H_Streetlight / S_Streetlight
To solve for H_Streetlight, we need to cross-multiply and solve for the unknown variable:
5 feet * S_Streetlight = 4 feet * H_Streetlight
H_Streetlight = (5 feet * S_Streetlight) / 4 feet
So, to find the proportion that could be used to determine the height of the streetlight, it would be:
5 feet / 4 feet = H_Streetlight / S_Streetlight
or
4/5 = S_Streetlight / H_Streetlight